Since PBS is "educational" can I use their material in the classroom?
PBS is a nonprofit organization that specializes in educational content. Most of their material is free and they encourage educators to use it. However, they do have some content that is only available for through purchase. As long as the content (i.e. DVDs, etc.) is legally aquired you most certainly can show it in the classroom.
Broadly speaking, you can show most website content to your class via a computer and projector without concern. The caution here is that the content has to be made freely available to the public, by the creator and/or host site of the content. (i.e., no logins, subscription fees, special licensing or terms of service, etc.)
Typical examples of free content include: